Renormalization is an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics.

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Momentum Space Renormalization of $\phi ^6 $ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d $ for the energy functional: $$ f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2 $$ where $\ d$ is the dimension ...
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Wilsonian vs 1PI

As a follow up to Difference between 1PI effective action and Wilsonian effective action, where can I find pedagogical material that highlights the similarities and differences between the 1PI and ...
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106 views

Convergence of light by light scattering amplitude

Perhaps I'm too exhausted to see the answer of why the photon-photon scattering should contain no divergences. In Peskin and Schroeder page 320 we find that because of the Ward identity the ...
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198 views

One-Loop Yukawa RGEs

I'm currently trying to understand how one can write the one-loop RGEs for the Yukawa couplings using the general formula: One example I'm interested in is how the author derives, using this ...
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What justifies the dependence of the coupling renormalization constant in the dimensional regularization regulator?

I wanna clarify some issues about renormalization in the $\bar{MS}$ scheme that I glossed over when I first learnt about this stuff. I am following http://arxiv.org/abs/1411.7853 section 3.1. The ...
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Is Bohmian Mechanics incompatible with loop corrections?

For those who continue to be unsatisfied with Quantum Mechanics (QM), Bohmian Mechanics (BM) is an alternative worth considering. It is sometimes claimed that BM is equivalent to QM, but Lubos Motl ...
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From Lagrangian to Feynman diagrams [closed]

Consider the the following Lagrangian of the $\phi ^4$ theory: $$\begin{align} \mathcal{L} = \frac{1}{2} [\partial ^{\mu} \phi \partial _{\mu} \phi - m^2 \phi ^2] - \frac{\lambda}{4!} \phi ^4 ...
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Does the 4/3 problem of classical electromagnetism remain in quantum mechanics?

In Volume II Chapter 28 of the Feymann Lectures on Physics, Feynman discusses the infamous 4/3 problem of classical electromagnetism. Suppose you have a charged particle of radius $a$ and charge $q$ ...
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Is the stability matrix of a linearised RG flow always diagonalisable?

This is a follow up on "Why are the eigenvalues of a linearized RG transformation real?". My question is simple: Is there some physical (or mathematical) reason for the stability matrix of ...
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779 views

List of known universality classes

I am working with RG and have a pretty good idea of how it works. However I have noticed that even though the idea of universality class is very general and makes it possible to classify critical ...
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How can dimensional regularization “analytically continue” from a discrete set?

The procedure of dimensional regularization for UV-divergent integrals is generally described as first evaluating the integral in dimensions low enough for it to converge, then "analytically ...
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Do perturbative renormalization groups help one understand when perturbation theory can be used in general?

If, as I asked in this question, a relevant operator in a renormalization group transformation can't be used in a perturbative expansion since it becomes large as the transformations are applied, does ...
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Equality of renormalized coupling constant

I want to show, that the renormalized coupling constants of a SU(N) Yang-Mills field with fermions included, are all equal. In the most textbooks it is written, that this could been shown by the ...
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Introducing cut-off in a renormalisation procedure for quantum mechanics

I've been reading a paper on renormalisation theory as applied to a simple one-particle Coulombic system with a short-range potential. In the process of renormalisation, the authors introduce an ...
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60 views

Logarithms in Renormalization

I am learning renormalization in Quantum field theory and following mainly Schwartz (Quantum field theory and standard model) for it. While explaining Renormalization group equations it says it mainly ...
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735 views

Zamolodchikov's c-theorem paper

I am reading the 1986 paper [1] where Zamolodchikov proves the c-theorem and I would like to understand how equations (7a), (7b) and (8) are derived from the Callan-Symanzik equation. For ...
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71 views

How to understand the idea of functional renormalization group?

I have been looking at how to use the functional RG method in many-body systems, but I don't quiet get the idea of it, it look different from Wilson's RG approach (eg. why shall we integrate out the ...
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414 views

Scalar field divergent mass correction interpretation question (hierarchy problem)

Simple power counting tells you that a scalar field coupled to some fermions at one-loop picks up a correction to the mass of the order $\Lambda^2$. Based on this people say things like "it's natural ...
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Superficial degree of divergence for scalar theories

I have a few questions regarding the derivation of the degree of divergence for feynman diagrams. The result is $$D = [g_E] - \sum_{n=3}^{\infty} V_n [g_n]$$ (following notation in Srednicki, $P118$) ...
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What does it mean by “infinities” when dealing with QFT? [closed]

I found this PDF online here while browsing Nobel Prize winner contributions, which explains a bit about renormalization (a concept for which Kenneth G. Wilson won the Nobel). However I was somewhat ...
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1-Loop Mass Splitting of vector-like Fermions

In this paper the author argues that for a vector-like fermion doublet, with degenerate mass $M$ at tree level, we always have a mass splitting between the charged component of the doublet $L$ and the ...
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Complex scalar field theory

For the complex scalar field theory $$L = -\partial_{\mu}\phi^{*}\partial_{\mu}\phi - m^{2}\phi^{*}\phi + J\phi^{*}+J^{*}\phi,$$ Why is there no factor of 1/2 in the lagrangian like in the real ...
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Renormalization Point for Coulomb Potential?

In Introduction to Quantum Field Theory by Matthew Schwartz at page 177 he explains that we use the renormalization point $p_0=0$ in order to derive Eq. 17.54: \begin{equation} \tilde{V}(p)= ...
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Apparent failure of SUSY nonrenormalization theorem

I am having trouble reconciling two pieces of information. Consider supersymmetric QED, i.e. a supersymmetric U(1) gauge theory with two chiral superfields of opposite charges, $h$ and $\hat{h}$. The ...
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What exactly is Weinberg's power counting theorem?

The massive gravity propagator goes like $\sim \frac{p^2}{m^4}$ at high energies and in this case we cannot apply Weinberg's standard power counting arguments. I have read something like that ...
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Decimation of a triangular lattice [closed]

Consider the network of spins shown below. The Hamiltonian is given by $$H = - \sum_{\langle i j k \rangle} [J \sigma_i \sigma_j \sigma_k + J_0]$$ with $J,J_o \geq 0$ and $\langle i j k \rangle$ ...
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Spinor field normalisation from poles in the propagator

In the theory of free scalar bosons (KG field) it is a basic result that the propagator $\Delta(p)$ has poles at $p^2=m^2$, with residue $1$ (or any other constant, depending on conventions). Thinking ...
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Structure of Mass Renormalisation

I'm currently working on the renormalisation part in Peskin, Schroeder QFT. There it is stated that non-logarithmic UV divergences give a mass renormalisation and thus are forbidden, e.g. for the ...
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29 views

Divergent diagrams in QED

I was reading about how to choose divergent diagrams in QED by using the concept of Superficial degree of divergence. We have an empirical relation $$ D= 4-E_b -\frac{3}{2}E_f $$ where $E_b$ is number ...
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Is a lagrangian with a background field interaction renormalizable ? If yes, when?

Consider the Lagrangian, $$ L = -\partial_{\mu} \chi \partial_{\nu} \chi^{\dagger} - m^2 \chi \chi^{\dagger} + g\chi \chi^{\dagger}\phi,$$ where $\phi$ is a background field and $\chi$ is a complex ...
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61 views

Cutoff-dependent “inverse propagator” for renormalization

In Zee's QFT in a Nutshell, when introducing mass renormalization, he calculates the "inverse propagator" for a $\phi^4$ scalar field theory to order $\lambda^2$ by considering the two diagrams shown: ...
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Counterterm Lagrangian and Renormalisation?

I am going through the notes on QFT by M. Srednicki (online: http://web.physics.ucsb.edu/~mark/qft.html), and I am having a hard time to understand the "renormalised" Lagrangian. Consider a ...
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Why would renormalization be necessary without divergent integrals? [duplicate]

Weinberg uses the LSZ reduction formula to introduce field renormalization,and on page 441, he says: As this discussion should make clear: the renormalization of masses and fields has nothing to ...
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Will Anderson's Poor Man's Scaling loose its effect when band width is small?

The s-d interaction Hamiltonian is as fellows $H_I=Js.S$, J is the coupling strength. We focus on the antiferromagnetic case, where $J>0$. According Anderson's poor man's scaling, the ...
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Resummation of large logarithms in effective field theory

I am trying to learn about the ideas of large-logarithms in effective field theory from a set of notes. However the following paragraph is confusing me: This doesn't seem quite right to me. Surely ...
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What is the problem with quantizing GR in the Effective Field Theory approach?

In the modern view due to Wilson, the cut-off $\Lambda$ is an intrinsic property of a theory and renormalization just means that the theory is invariant under scale transformations below $\Lambda$. ...
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Running coupling, effective potential and the stability of vacuum

Consider the potential $$V(\phi)=\frac{1}{2}\mu^2\phi^2+\lambda\phi^4$$ where $\phi=\phi(t,\textbf{x})$ is a real scalar field. Let, $\mu^2<0$ and $\lambda>0$ then the potential is bounded from ...
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Questions about the beta function in QFT

When someone defines $\beta(g)=\mu\frac{dg}{d\mu},\quad (1)$ he is implicitly assuming that the result of the rhs of this equation can be written only in terms of $g$ instead of $\mu$, which is not ...
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Are the bare parameters of a renormalizable field theory infinitesimal or infinite?

I think this should be an easy question. Several sources I've read say that the bare parameters in a quantum field theory are "infinite" so that the renormalized values are "finite". However, in ...
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Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)?

I am learning DMRG recently. I noticed there are many papers both in the DMRG approach and MPS (such as variational matrix product state (VMPS) by F.Verstraete and J.I.Cirac) approach. In my eyes, ...
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Why is quantising gravity so difficult? [duplicate]

Since gravity is so similar with the Yang-Mills theory, the Christoffel connection is the gauge potential, the Riemann curvature is the field strength, then why is quantising gravity so difficult when ...
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What should I think of a diverging beta function (in Renormalisation Group flow)?

I have written a set of RG flow equations using Functional Renormalisation Group methods. I am looking at the flow of a well known problem with an additional original coupling. I did not do anything ...
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Meaning of counterterms and quantum corrections

When one talks about the “classical Lagrangian” of a field, does one mean the tree-level Lagrangian with physical masses and physical couplings? If yes, does it therefore mean that the bare ...
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Top quark mass $m_t$ at energy scales $\mu < m_t$?

Edit - Maybe formulated differently: Does it make sense to talk about the top mass at energies below $m_t$, although in all processes the corresponding energy scale is above $m_t$, because of the rest ...
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Dimensional Regularization for $\phi 4$ theory

When using dimensional Regularization for $\phi 4$ theory to calculate the running of the mass, why there is no quadratic divergence as expected? For details, cf ...
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What is “the scale at which a theory is defined”?

I'm trying to learn the renormalization group, but I am confused about renormalization schemes. The general idea of RG is that physical predictions are independent of "the scale at which a theory is ...
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How do people go about looking for asymptotic safety in quantum gravity?

Do we have (proposed?) methods to look for fixed points in the renormlaization group flow of the Einstein-Hilbert action? My understanding of the RG is still somewhat sketchy at this point and I am ...
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Numerically extracting free energy in renormalization procedure

I have some doubts about how to apply real space renormalization numerically. I understand the theoretical concept, and how we require $Z'=Z$, being $Z'$ the partition function of the renormalized ...
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Computing the pole mass from a given $\overline{MS}$ mass?

Given a Yukawa coupling as a function of scale $\mu$ and a vev, therefore $m_R(μ)=Y(μ)⟨ϕ⟩$, how can I compute the corresponding pole mass $m_p$? Relations I was able to find are (page 39) ...
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Renormalisation group equation for Green's functions

The renormalization group equations for the $n$-point Green’s function $$\Gamma(n) = \langle \psi_{x_1} \dots \psi_{x_n}\rangle $$ in a four-dimensional massless field theory are $$\mu \frac{d}{d ...